Why doesn't water burn?

In chemistry we define the word burn to mean: "to undergo combustion, either fast or slow; to oxidize." So when gasoline "burns", the carbon and hydrogen atoms in the gas rapidly combine with oxygen atoms in the air to form CO2 and H2O. When charcoal "burns", the carbon atoms in the chacoal combine with oxygen atoms in the air to form CO2. When iron or steel "burns", the iron atoms in the piece of iron combine with oxygen atoms in the air to form rust. Normally the process is very slow. But if you create small enough pieces of iron, like that seen in steel wool, the burning happens quite quickly, like this:

If you spin a big piece of burning steel wool in the air, it will create a huge cascade of flying sparks as the steel quickly burns. (I'm not recommending that you do this - but people do do it. Search on YouTube sometime.)

So, why won't water burn? It's because the burning has already happened. When the hydrogen reacted with oxygen - in other words, when the hydrogen "burned" - water was the result.

A side question - why is water good at extinguishing some types of fire - for example wood and paper fires? The water absorbs into the wood or paper and blocks the flow of oxygen. The water also cools the burning wood or paper down well below its flash point.